### Abstract

Let T be an ergodic transformation of a nonatomic probability space, f an L_{2}-function, and K ≥ 1 an integer. It is shown that there is another L_{2}-function g, such that the joint distribution of T ^{i} g, 1 ≤ i ≤ K, is nearly normal, and such that the corresponding inner products (T^{i} f, T^{j} f) and (T ^{i} g, T^{j} g) are nearly the same for 1 ≤ i, j ≤ K. This result can be used to give a simpler and more transparent proof of an important special case of an earlier theorem [3], which was a refinement of Bourgain's entropy theorem [9].

Original language | English (US) |
---|---|

Pages (from-to) | 75-82 |

Number of pages | 8 |

Journal | New York Journal of Mathematics |

Volume | 4 |

State | Published - May 21 1998 |

### Keywords

- Bourgain's entropy theorem
- Gaussian processes
- L2-processes

## Fingerprint Dive into the research topics of 'Approximation of L<sup>2</sup>-processes by Gaussian processes'. Together they form a unique fingerprint.

## Cite this

Akcoglu, M. A., Baxter, J. R., Ha, D. M., & Jones, R. L. (1998). Approximation of L

^{2}-processes by Gaussian processes.*New York Journal of Mathematics*,*4*, 75-82.